Questions: Choose the system of equations that matches the following graph: 2x + 4y = 0 7x - 6y = -24 2x - 4y = 0 7x + 6y = -24 2x - 4y = 0 7x - 6y = -24 2x + 4y = 0 7x + 6y = -24

Solution Steps

Two points on the red line are (-4, -2) and (0, 4).

The slope of the red line is (4 - (-2))/(0 - (-4)) = 6/4 = 3/2. Using the point-slope form, the equation of the red line is y - 4 = (3/2)(x - 0), which simplifies to y = (3/2)x + 4. Multiplying by 2 gives 2y = 3x + 8, or 3x - 2y = -8. This equation is equivalent to neither 2x + 4y = 0 nor 2x - 4y = 0, so we must modify it. Multiplying 3x - 2y = -8 by -2/3 gives 7x+6y = -24. Multiplying by -2 gives 2x + 4y = 0.

Two points on the blue line are (0, 0) and (4, 2).

The slope of the blue line is (2 - 0)/(4 - 0) = 1/2. Since the line passes through the origin, its equation is y = (1/2)x. Multiplying by 2 gives 2y = x or x - 2y = 0. This line does not match 7x - 6y = -24 or 7x + 6y = -24. Multiplying x - 2y = 0 by 7 gives 7x - 14y = 0.

The first option has 2x + 4y = 0 and 7x - 6y = -24, which matches the red line (after modification) but not the blue line. The second option has 2x - 4y = 0 and 7x + 6y = -24. Again the equations appear correct for the red line but not the blue. The third option is 2x - 4y = 0 and 7x - 6y = -24. These are incorrect. The fourth option is 2x + 4y = 0, which can be multiplied by -1/2 to get x + 2y = 0 and 7x+6y=-24 which resembles the second option and matches the red line but not the blue line.

Final Answer